What has changed is the cursor of time has moved onto a different version of the person with a different view of a different 'now'.

But the past person and past view are static and the current person and current view are static - when considered from a 4d spacetime perspective.

Okay, but then the view is changing, and the view is part of the reality, isn't it? — Terrapin Station

But at any given moment, we are static and our view is static.

Then there is the next moment, the view is different but we and the view are still static.

So nothing is changing from the perspective of a static 4D universe.

My knowledge of QM is very limited, but I think that the wave function collapses to a 'particle' when measured - at least for particles like the photon. A very small, collapsed, wave could be mistaken for a point particle? It would seem neat and tidy if all particle types had similar behaviour in this regard (string theory comes to mind). But probably we have to stick with uncollapsed waves from what you are saying. They could still be centred on a discrete grid point though.

I think that our theories use continuous variables as an excellent approximation for a reality that is discrete on such a fine level that it appears continuous to us (and thus continuous theories give results very close to reality). So continuous calculus gives good results but does not reflect the micro nature of reality correctly. This seems to be how classical physics works - the classical approximation of (what we now know to be) discrete matter are good enough because discreteness of matter only manifests its effects in the micro world.

I believe that if we ever hit on a ToE then it will be a discrete theory and utterly useless for predicting behaviours in the macro world - a quantum theory of gravity would never be used to try to predict the orbits of the planets for example - we would stick with Newton/Einstein for that. It would be useful in understanding the early moments of the Big Bang though.

Not sure what you mean?

Imagine sitting still in front of window watching the world go by. The view changes but you do not. So we would be part of reality and unchanging - but we'd see the ever changing 'now' view of the world.

Change can't be an illusion, because the illusion(s) change. — Terrapin Station

If we only perceive part of reality (now) but all of reality actually exists in some unchanging form (past, present, future) then change would seem to be an illusion - nothing changes in reality - it is just what we are looking at that changes.

If you think of it as all existing and then there is a 'cursor of now' that moves across time - and we always see 'now' rather than past/future then it could be argued that we are not changing - the only thing that changes is the 'now' cursor - everything else is static.

I think that there would be an unchanging, timeless aspect to the environment I mentioned - it would support uncreated brute facts. But when a brute fact performs an act, the environment is extended. So that would allow brute facts and change to co-exist. So it would be that something like time is there but it is optional in a sense.

Another possibility is future real eternalism - then change is just an illusion and everything has already happened in some sense - a completely static 4D brick of a universe containing God, us and spacetime. But its a hard sell...

It could be the timeless environment is like growing block universe maybe. So part of it has permanent, unchanging existence, but it can 'grow' to allow change of some form.

It could be that the wider universe is a different type of container to spacetime with different rules.

My argument is the existing 'forever' in time is not possible. Introducing a second, similar type of time (call it time2), leads to the same conclusion - existing forever in time2 is impossible. This regress of times must terminate with some sort of non-time like environment in which both brute facts are possible and change is possible. That is a challenge I admit, but IMO that is what the logic points to.

Maybe God is non-material and so does not need anything like time to effect change.

I think that time has a start so something physical changed when we went from a no-time to time situation, so time is something physical (as in a container: spacetime).

Being "outside of time" wouldn't imply anything about being creation or destruction. It would only imply something that can't move/change at all. If it's possible for there to be existents that can't move/change at all, that could be possible for any arbitrary existent, right? — Terrapin Station

It is a challenge I admit. I think that the human race may have a limited understanding of reality - we are familiar only with spacetime and 'spacetime events'. Of everything in reality (and my argument is that there is a wider reality than just spacetime), it maybe that humans understand only a tiny fraction of it.

So the arguments for a start of time imply that timeless change must be possible - at least one causally effective agent seems to be required - but I cannot claim to understand how it works. It is argued sometimes that God exists in the 'eternal now' - our usual conception of effect following cause may not hold:

- God IS formulating a plan for spacetime
- God IS creating spacetime
- God IS finished creating spacetime

All these event, in some sense, from the perspective of a timeless being, might be happening concurrently.

If you think that works for everything, then it's necessary for you to have things always existing. — Terrapin Station

I should have said: 'to be X in time, something has to start X'.

Things outside of time do not have a temporal start or end, they are not created or destroyed, they just ARE.

I think it's because he has the aim of arriving at a particular conclusion (a religious conclusion), and the arguments are basically ad hoc means of getting to the conclusion he wants. — Terrapin Station

Deism is technically a non-religious belief. Because of considerations like the fine tuning argument, it seems to me that deism is the most likely explanation for the way things are, that's why I pursue it.

I am actually on the rocks with regards to Monotheism Vs Polytheism. There are arguments that there must be a first cause / a brute fact - so it maybe possible to prove there is at least one god. But disproving the existence of many brute facts (IE potentially many gods) is impossible I think. Disproving existence can only be achieved if it is possible to show existence results in a contradiction. Try disproving the existence of unicorns for example... it's impossible.

So I think deism will always remain a belief rather than something that can be proved.

If something is bigger than everything possible, then it expands, then it cannot have have been bigger than everything possible to begin with.

I am a finitist and I do not believe in different sizes of infinity - a minority viewpoint.

I think that 'potential infinity' is a very useful concept in science/maths. It is 'actual infinity' that bothers me.

The universe expanding and the universe being actually infinite seem to me contrary.

So he is eternal and travels back in time forever counting. From our perspective - it has all actually happened - it is history - every number has been counted - a completed infinity

But as you mention, it's impossible to count to infinity (from the traveller's perspective, its impossible to get more than 0% of the way to counting to infinity).

I guess to me infinity does not make sense as a concept, perhaps this scenario brings that out.

Thanks. I am not sure what size the actual universe is - very large but I suspect it must be finite in both time and space. An idea I've been playing with:

Imagine a backwards travelling, counting, eternal, time traveller. Assume that past time is infinite. Then the traveller, should have, from our perspective, counted every number! If this is not an actually completed infinite process, I’m not sure what would qualify. But it is impossible to count all numbers - no matter how many you count, you are always 0% of the way to completion. So it seems that even given an actual, completed infinity of time, actual infinity is not realisable/completable. Which makes me think an actual infinity of time is impossible.

This argument here actually supports a cyclical universe that has been here forever, as the universe cannot be the reason for itself — Mark Dennis

As I already mentioned, a cyclical universe still needs a start of time - something has to set the 'now' cursor of time in motion around the circle of time.

If it "has existed eternally" then sure, those words conventionally refer to there being no start to it. And indeed it wouldn't have a starting state then, because of what "start" refers to. But this doesn't imply that something can't have existed forever. It just wouldn't have a "start + n" state, because there's no start to it. Again, that's what "existed forever" refers to--there's no start. — Terrapin Station

In general: 'to be X something has to start X' works for everything - counting, talking, spinning, oscillating and ultimately existing. Infinity does not have the ability to cause something to exist 'by magic' - to exist, something has to start existing.

As always, by the way, you either have something existing forever or you have something spontaneously appearing "out of nothing" so to speak. Neither seems intuitively right, but there's no way around those being the only two options. — Terrapin Station

I think that the start of time was the Big Bang. Matter either came into existence via the zero energy universe hypothesis or matter entered time (at the point of the Big Bang). Neither qualify as 'something from nothing'.

So the proposition "(Principle of Sufficient Reason - everything in time has a cause/reason)" cannot be used as evidence of the beginning of the universe because it comes from this very conclusion. If the proposition is only true if the conclusion is true, then we are going to have some very sticky problems grounding this argument logically — Mark Dennis

My argument does not rely on the PSR, but I think an altered version of the PSR is supportive of my argument:

- Everything in time has a reason
- Nothing can be the reason for itself

I think this is more reasonable than Leibniz's original and it points to a minimum of one 'brute fact'. I'd argue that brute facts can only exist outside of time.

Why would you say that we have to be determinists? — Terrapin Station

Even if reality is not fully deterministic, there is still a relationship between prior and subsequent states - if the prior state does not exist then the subsequent state does not exist.

So for a non-deterministic eternal particle, I would argue it has no start (because it existed 'forever') so it cannot have a start+1 state, a start+2 state, so by induction, it can't exist.

So, there is no such thing as forever, because it doesn’t have an initial state. And if it did it wouldn’t be forever. — Brett

That's the crux of my argument.

To clarify, I mean spacetime cannot have existed 'forever' - nothing can exist 'forever' within time - if you disagree with this statement, you should provide a counter argument to the argument I gave in the OP.

But something (the wider universe) can exist permanently outside of time - I say 'permanently' rather than 'forever' as the second term has no meaning in the absence of time.

I'm not sure where your comments went. Maybe the spam filter got them - you could ask the moderator. Still my reply is:

Beginnings I think are something we as humans project onto the universe because we can verify our own individual non-existence — Mark Dennis

I think that matter and energy need a temporal start to exist in spacetime. For example, a matter particle has position and momentum as state. The current state is determined by the previous state of the particle. If there is no first state (because it existed 'forever') all the subsequent states are undefined and the particle cannot exist.

See this is what I mean, In order to explain a universe of spacetime with a beginning you've used a something (A wider timeless universe) to explain it. So no nothing. Where is the start supposed to have been? — Mark Dennis

I did not say there was ever nothing - I said that the universe cannot have existed 'forever' in time. The timeless universe is timeless - it has no start or end - it just 'IS' - it has permanent existence.

It exists as an uncaused brute fact. For anything to exist at all, causality requires at least one brute fact. Brute facts cannot exist within time (Principle of Sufficient Reason - everything in time has a cause/reason) - so they must exist without time - else there would really be nothing.

Circular time is an interesting possibility. I think there is something different from 'now' compared to past and future - else we would perceive now/past/future in the same way which we clearly don't. So with an eternalist circular time model, there must be some sort of pointer/cursor to the current time. That cursor would circle around the loop of time. But that cursor must have started circling at some point - which still seems to require a 'start of time'.

I don't see how god comes into it really as I don't believe in a creator god. — Mark Dennis

I am just using a god as a thought experiment to demonstrate the non-sensical nature of the universe existing 'forever' - an eternal clock can be substituted instead. I did not really want to get into a discussion of God on this thread as people get emotional and it clouds the issue.

Without a creator god, what can bring about a something from nothing? The god itself would have to be a something and therefore there wasn't nothing, there was god. — Mark Dennis

Matter was either created at the start of time (see the Zero Energy Universe Hypothesis) or entered time at the start of time. Both possibilities are consistent with the Big Bang and neither is 'something from nothing'.

There was never a time outside of the beginning of time for there to be no time. Therefore time has always been. Same with the universe, there was never a time where there was a nonexistence and then existence. So whether the universe is cyclical or not, the universe has always been here. It's the only place that can have an always. — Mark Dennis

I think that we should distinguish between spacetime (which seems to have come about at the Big Bang) and a wider, timeless universe (which seems likely to have given birth to spacetime via the Big Bang). Human experience says that time is required for events to happen. But more specifically, spacetime is required for spacetime events to happen. It is likely that of all the things in the wider universe, the human race is only aware of a tiny fraction. So events beyond spacetime I think are possible - they would just be of a different nature that is not understood by the human race.

Yes, the Big Bang is conventionally seen as the start of spacetime.

Yes I have perhaps not made myself clear. If we talk about spacetime as the thing that was created in the Big Bang, then there is a wider universe that contains spacetime and that wider universe would have 'given birth' to spacetime.

The cause of the Big Bang is not known - all we have is an impossible prediction of the singularity (infinite density) from general relativity. The intense gravity involved suggests that time would slow to an almost stop. The Big Bang happened about 14 billion years ago. There is some debate over whether it took place at a single spacial location (I believe it did).

There are pre-Big Bang cosmologies too but the most successful is Eternal Inflation and that has a definite start so would also be compatible with a start of time (its eternal in the sense of future rather than past time). Other less successful cosmologies (like CCC) have the universe as eternal in time so are obviously not compatible with a start of time.

The start of time would give everything an initial state from which it could derives its subsequent states - it would give everything its 'realness'.

Matter was either created at the start of time (see the Zero Energy Universe Hypothesis) or entered time at the start of time. Both possibilities are consistent with the Big Bang (the obvious candidate for the start of time).

A start of time.

I think it is not necessary to fill space (as in a space-filling polyhedron like a cube). I am more imagining a grid of zero dimensional points in space. The particle, which has a non-zero dimension, would be centred on one of the grid points. If there are two neighbouring particles, they would not be in contact with each other, so space is not filled. Particles would move from point to point in the grid rather like the electron performs a quantum jump from one orbit to another - not passing between any intermediate space.

With QM, we have waves (and I suspect a particle is just a compressed wave) and so the waves would be centred on one of the grid points.

All of this would take place down near Planck length, so the universe would appear completely continuous to us.

Loop quantum gravity - the competitor of string theory - has space as discrete.

Discrete means that is made of parts that are distinct from each other: it can be finite, but not necessarily. The set of natural numbers is discrete but infinite. — Mephist

In this instance, I am referring to finite distances of space. If a finite distance of space is also discrete then it cannot be decomposed into infinite sub-sections.

Galileo's paradox is about positive integers, not about continuous sets. In fact, I believe that the idea of a "continuous set" had not even been invented in XVII century. For what I know, Euclidean geometry never speaks about a line being a set of points: for Euclidean geometry, 1-dimensional objects (lines) are a completely different kind of things then discrete (countable) objects. And Galileo does not even consider the idea that a line can be made of a set of distinct objects. For what I know, the idea of continuous (uncountable) sets was invented after Cantor, 200 years after Galileo. — Mephist

I think Galileo's paradox is applicable to continua. For example, to establish a one-to-one mapping between two continua:

{0, 1} maps to {0, 2}
{0, 1/2, 1} maps to {0, 1, 2}
{0, 1/4, 1/2, 3/4, 1} maps to {0, 1/2, 1, 3/2, 2}
etc...

At the same time we can note that 0->1 is half the length of 0->2. So Galileo's paradox appears to apply - the continua are equal in terms of a one-to-one mapping but unequal in terms of one being twice the length of the other.

So, if I understand correctly, you are trying to prove that the set of point of a line is finite (not countably infinite). Is it right?

If that's what you are arguing (that a line is made of a finite set of points), the obvious question is: how many points there are in a given segment? — Mephist

Yes I suspect that space is discrete... proving it would be nice (so would winning the lottery!).

If reality is discrete and a line segment (in reality) is composed of points (or fixed sized line segments) then the length of each point/sub-segment is some number greater than zero. The Planck length is often mentioned in this regard.

The argument that you are making with the limits assumes that space is infinite but discrete, right? — Mephist

A piece of space is discrete if it allows only a finite number of possible positions (points). So I've assumed an infinite number of possible positions - if its not discrete, it must be continuous. From Wikipedia:

"Formally, a linear continuum is a linearly ordered set S of more than one element that is densely ordered, i.e., between any two distinct elements there is another (and hence infinitely many others), and which "lacks gaps" in the sense that every non-empty subset with an upper bound has a least upper bound."

So all continua are (in the above sense) alike in that they can be subdivided forever, so we can write:

points(0,1) = points(0,2)

At this point, there is a one-to-one correspondence between the left and right side so they have the same 'size' so the equals sign seems maybe justified.

points(0,1) = points(0,1) + points(1,2)

Now there is a still a one-to-one correspondence between the left and right side, however, when it is written like this, it appears to part from common sense. I know this corresponds to the convention ∞=∞+∞. I also know that if two things are identical and you change one of them, then they cannot be identical anymore.

I just cannot get my head around continua, they just seem impossible. It is possibly the use of the equals sign to represent a one-to-one correspondence that is the problem. It maybe that it is invalid logically to write:

points(0,1) = points(0,2)

It comes back to Galileo's paradox - the above are equal in the sense of a one-to-one mapping but at the same time, one is clearly twice the other. I think that it is not valid to compare the size of two infinities (as Galileo believed) - they are fundamentally undefined so have no size and cannot be compared. If something never ends, then it can never have a size and never be fully defined. I do not believe Cantor has added anything our the understanding of infinity - he has detracted from it - Galileo was on the right lines.

So coming back to my original starting place, my assumption that one of the following must be true:

1. points(0,1) = points(0,2)
2. points(0,1) < points(0,2)
3. points(0,1) > points(0,2)

seems incorrect. It seems I should instead have written:

1. UNDEFINED != UNDEFINED
2. UNDEFINED !< UNDEFINED
3. UNDEFINED !> UNDEFINED

So I think that maths cannot model actual infinity or continua. Does that mean these things do not exist in the real world? I think that maybe the case. If continua exist, then that implies that the informational content of 1 light year of space is the same as the informational content of 1 centimetre of space - in the sense that both 'containers' record the position of a particle to an identical, infinite, precision. This flaunts 'the whole is greater than the parts'. I trust that axiom more than I trust Cantor's math.

I’d like to show that space must be discrete, but my maths is not so great. Maybe one of our resident mathematicians can comment?

I’m considering the number of points between 0->1 and 0->2. I’ll denote these as functions: points(0,1) and points(0,2).

One of the following must hold true:

1. points(0,1) = points(0,2)
2. points(0,1) < points(0,2)
3. points(0,1) > points(0,2)

I think by common sense, we can eliminate [3] and focus on [1]:

points(0,1) = points(0,2)
points(0,1) = points(0,1) + points(1,2)

If there is a finite number of points in each interval, space must be discrete, so I will assume an infinite number of points in each interval:

$\lim_{n\rightarrow\infty} n = lim_{n\rightarrow\infty} n + lim_{n\rightarrow\infty} n$
$\lim_{n\rightarrow\infty} n = 2 lim_{n\rightarrow\infty} n$
(1+1+1+1+…) = 2 x (1+1+1+1+…)
1 = 2

This last step, dividing though by ∞, is not conventionally allowed, presumably because it’s argued that there are different kinds of infinity. I would have thought (wrongly?) that because I am dividing though by an identical kind of infinity to the infinity in the expression then it should be allowed?

So [1] does not seem possible, that just leaves [2]:

points(0,1) < points(0,2)

Which makes sense, but it implies that space cannot be a true continuum. There are more points in the larger interval implying that the larger interval is structurally different to the smaller interval, whereas for a true continuum, they must be identically structured.

It could be that a point is not the fundamental unit of space, but the argument I think would be identical for a segment.

No, it doesn’t. Your definition says ‘greater than 0% probability’. That means you only need ONE instance to place it above 0% probability. A probability of 0.000000000000000000001% is still greater than 0%. — Possibility

OK but is stands out like a sore thumb compared to all the other natural events (that happen multiple times) - sufficient to be very suspicious about labelling it natural.

Yes, it was discovered - by humans. But all animals (and many chemical reactions) have at least been aware of it to some degree. — Possibility

I believe time is a creation. Causality requires the minimum of one uncaused, brute fact to act as the tip of the causal pyramid and cause everything else. It is only possible to exist as an uncaused brute fact if you exist outside time; existing 'forever' inside time is logically impossible (cannot exist with no temporal start).

That implies timeless thing(s) exist. The timeless thing(s) must have caused the creation of time.

The BB seems to support this view - it looks a lot like the start of time what with time slowing down due to the intense gravitational field.

I’m not sure what ‘the FTA’ refers to — Possibility

Fine Tuning Argument.

3. Who said? Maybe that's your personal problem. In any case it is defined as the first transfinite cardinal. That is, not an integer. And not a natural number. — tim wood

Any size of a set must be a natural number. So the definition of Aleph-naught as 'not a natural number' is plainly contradictory.

Tim you are a f**king idiot.

I have a question:

"computable functions are exactly the functions that can be calculated using a mechanical calculation device given unlimited amounts of time and storage space"

https://en.wikipedia.org/wiki/Computable_function

It strikes me that it is impossible to specify a function that a computer could execute that would result in actual infinity as the output? No amount of successive addition or multiplication yields actual infinity.

The definition of Aleph-naught is contradictory:

1. Aleph-naught is the size of the set of naturals
2. Sets contain a positive number of whole items only
3. So Aleph-naught must be a natural number
4. But there is no largest natural number
5. So Aleph-naught cannot exist (or be larger than all the natural numbers)

Transfinite numbers are not infinity. Infinity is not a transfinite number. — tim wood

"Transfinite numbers are numbers that are "infinite" in the sense that they are larger than all finite numbers, yet not necessarily absolutely infinite. The term transfinite was coined by Georg Cantor, who wished to avoid some of the implications of the word infinite in connection with these objects, which were, nevertheless, not finite. Few contemporary writers share these qualms;it is now accepted usage to refer to transfinite cardinals and ordinals as "infinite". However, the term "transfinite" also remains in use."

- https://en.wikipedia.org/wiki/Transfinite_number

???

That's what all the mathematicians say. — tim wood

You will have to explain that.

I believe there is constructivism - a minority view in maths - which rejects actual infinity.

I believe the vast majority of mathematicians accept actual infinity as a number - see the transfinite numbers from set theory.

A thought experiment:

1. Imagine a backwards travelling, counting, eternal, time traveller
2. Assume that past time is infinite (I do not think it is, but for the sake of argument)
3. Then the traveller, will from our perspective, have counted every number
4. Seems unbelievable (no greatest number), but thats the nature of infinity
5. If this is not an actually infinite process, I’m not sure what would qualify?
6. Every number has been counted and no number corresponding to 'actual infinity' has been encountered
7. So it seems we can conclude that actual infinity is not a number?

This is why I asked you clarify whether by ‘unnatural’ you meant supernatural or metaphysical. — Possibility

- Natural is something that has a greater than 0% probability of occurring naturally.
- Unnatural is something that has a 0% probability of occurring naturally.

Something that is unnatural - not of nature - I guess is synonymous with supernatural.

The BB, if it were a natural event and time were infinite, would have occurred an infinite number of times at each point in space.

I'm glad you agree that time is finite. Still, one instance only of BBs over the last 14 billion years seem to place it firmly in the unnatural camp (using the above definitions).

Another way to define it is nature is spacetime. Spacetime must of been created by something beyond space time. Something unnatural.

It’s not a matter of an intelligent agent ‘creating’ another dimension, but of first interacting with something beyond what we understand, and then gradually developing awareness of it despite the lack of understanding. — Possibility

That suggests to me that the additional dimension of time was discovered rather than created?

What do you mean by ‘intelligent’? — Possibility

I guess I just mean capable of rational thought and resulting independent actions.

In my opinion there is no need to venture beyond what is ‘natural’ for your ‘intelligent agent’ - on weight of evidence. — Possibility

The creation (or discovery) of time, the FTA, etc... seem to imply a timeless intelligence external to spacetime. I would define that as an unnatural intelligence.